Segmented carbon radial or circumferential seals have been employed in a number of environments associated with compressible fluids, such as gases. They have been used, for example, in connection with gas turbine engines. Such radial seals typically act to, among other things, seal high pressure areas from low pressure areas. For some applications, Rayleigh steps or pads have been included to generate hydrodynamic opening force that enables a segmented seal to operate in a “non-contact” condition. The hydrodynamic opening force generated by a plurality of pads can distribute the associated force more evenly along a circumferential direction providing, among other things, a better balancing of forces. However, it has been found that an abrupt flow transition can occur with respect to the entrance of Rayleigh steps or pads and the transverse groove that helps to provide appropriate pressure balance. An abrupt transition between the transverse groove and the steps or pads can, among other things, cause associated flow losses and reduced efficiency.